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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.01345 |
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| _version_ | 1866915982257160192 |
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| author | Hikawa, Tatsuro |
| author_facet | Hikawa, Tatsuro |
| contents | The $ (k, a) $-generalized Fourier transform $ \mathscr{F}_{k, a} $ introduced by Ben Saïd--Kobayashi--Ørsted is a deformation family of the classical Fourier transform with a Dunkl parameter $ k $ and a parameter $ a > 0 $ that interpolates minimal representations of two different simple Lie groups. In the present paper, we focus on the case $ a < 0 $. As a main result, we find a unitary transform that intertwines the known case $ a > 0 $ and the new case $ a < 0 $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $(k, a)$-generalized Fourier transform with negative $a$ Hikawa, Tatsuro Representation Theory 43A32, 22E46 The $ (k, a) $-generalized Fourier transform $ \mathscr{F}_{k, a} $ introduced by Ben Saïd--Kobayashi--Ørsted is a deformation family of the classical Fourier transform with a Dunkl parameter $ k $ and a parameter $ a > 0 $ that interpolates minimal representations of two different simple Lie groups. In the present paper, we focus on the case $ a < 0 $. As a main result, we find a unitary transform that intertwines the known case $ a > 0 $ and the new case $ a < 0 $. |
| title | $(k, a)$-generalized Fourier transform with negative $a$ |
| topic | Representation Theory 43A32, 22E46 |
| url | https://arxiv.org/abs/2407.01345 |